- In Refereed Journals (submitted, accepted or published)

- 42) A. Chen, F. Li, Y. Cheng, An ultra-weak discontinuous Galerkin method for Schrodinger equation in one dimension, submitted, April 2018
- 41) P. Fu, Y. Cheng, F. Li, Y Xu, Discontinuous Galerkin methods with optimal L2 accuracy for PDEs with high order spatial derivatives, submitted, March 2018
- 40) V. A. Bokil, Y. Cheng, Y. Jiang, F. Li, P. Sakkaplangkul, High spatial order energy stable FDTD methods for Maxwell's equations in nonlinear optical media in one dimension, [PDF], Journal of Scientific Computing, in print, 2018
- 39) P. Fu, F. Li, Y. Xu, Globally divergence-free discontinuous Galerkin methods for ideal Magnetohydrodynamics equations, submitted, October 2017
- 38) V. A. Bokil, Y. Cheng, Y. Jiang, F. Li, Energy stable discontinuous Galerkin methods for Maxwell's equations in nonlinear optical media, [PDF], Journal of Computational Physics, v350 (2017), pp.420-452
- 37) H. Yang and F. Li, Discontinuous Galerkin methods for relativistic Vlasov-Maxwell system, [PDF], Journal of Scientific Computing, v73 (2017), pp.1216-1248
- 36) M. Li, P. Guyenne, F. Li, L. Xu, A positivity-preserving well-balanced central discontinuous Galerkin method for the nonlinear shallow water equations, [PDF], Journal of Scientific Computing, v71 (2017), pp.994-1034
- 35) Y. Cheng, C.-S. Chou, F. Li, Y. Xing, L2 stable discontinuous Galerkin methods for one-dimensional two-way wave equations, [PDF], Mathematics of Computation, v86 (2017), pp.121-155.
- 34) M. Li, F. Li, Z. Li, L. Xu, Maximum-principle-satisfying and positivity-preserving high order central DG methods for hyperbolic conservation laws, [PDF], SIAM Journal on Scientific Computing, v38 (2016), pp.A3720-A3740
- 33) Z. Tao, F. Li, J. Qiu, High-order central Hermite WENO schemes: dimension-by-dimension moment-based reconstructions, [PDF], Journal of Computational Physics, v318 (2016), pp.222-251
- 32) F. Long, F. Li, X. Intes, S.P. Kotha, Radiative transfer equation modeling by streamline diffusion modified continuous Galerkin method, [PDF], Journal of Bio-optical, v21 (2016), 036003
- 31) H. Yang and F. Li, Stability analysis and error estimates of an exactly divergence-free method for the magnetic induction equations, [PDF], ESAIM: Mathematical Modelling and Numerical Analysis, v50 (2016), pp.965-993
- 30) Z. Tao, F. Li, J. Qiu, High-order central Hermite WENO schemes for hyperbolic conservation laws, [PDF], Journal of Computational Physics, v281 (2015), pp.148-176
- 29) T. Xiong, J. Jang, F. Li, J.-M. Qiu, High order asymptotic preserving nodal discontinuous Galerkin IMEX schemes for the BGK equation, [PDF], Journal of Computational Physics, v284 (2015), pp.70-94
- 28) J. Jang, F. Li, J.-M. Qiu, T. Xiong, High order asymptotic preserving DG-IMEX schemes for discrete-velocity kinetic equations in a diffusive scaling, [PDF], Journal of Computational Physics, v281 (2015), pp.199-224
- 27) M.A. Reyna and F. Li, Operator bounds and time step conditions for DG and central DG methods, [PDF], Journal of Scientific Computing, v62 (2015), pp.532-554 (Note: correction is made to definition 9 on page 10)
- 26) J. Gopalakrishnan, F. Li, N.-C. Nguyen, J. Peraire, Spectral approximations by the HDG method, [PDF], Mathematics of Computation, v84 (2015), pp.1037-1059.
- 25) H. Yang and F. Li, Error estimates of Runge-Kutta discontinuous Galerkin methods for the Vlasov-Maxwell system, [PDF], ESAIM: Mathematical Modelling and Numerical Analysis, v49 (2015), pp.69-99.
- 24) J. Jang, F. Li, J.-M. Qiu, T. Xiong, Analysis of asymptotic preserving DG-IMEX schemes for linear kinetic transport equations in a diffusive scaling, [PDF], SIAM Journal on Numerical Analysis, v52 (2014), pp. 1497-2206
- 23) M. Li, P. Guyenne, F. Li, L. Xu, High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model, [PDF], Journal of Computational Physics, v257 (2014), pp.169-192
- 22) Y(ingda). Cheng, I. Gamba, F. Li, P. Morrison, Discontinuous Galerkin methods for Vlasov-Maxwell equations, [PDF], SIAM Journal on Numerical Analysis, v52-2 (2014), pp. 1017-1049 (see arxiv:1302.2136 for a long version)
- 21) H. Yang, F. Li, J. Qiu, Dispersion and dissipation errors of two fully discrete discontinuous Galerkin methods, [PDF], Journal of Scientific Computing, v55 (2013), pp.552-574
- 20) Y(ue). Cheng, F. Li, J. Qiu, L. Xu, Positivity-preserving DG and central DG methods for ideal MHD equations, [PDF], Journal of Computational Physics, v238 (2013), pp.255-280
- 19) S. Yakovlev, L. Xu, F. Li, Locally divergence-free central discontinuous Galerkin methods for ideal MHD equations, [PDF], Journal of Computational Science, v4 (2013), pp.80-91. (Special issue on Computational Methods for Hyperbolic Problems)
- 18) F. Li and L. Xu, Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations, [PDF], Journal of Computational Physics, v231 (2012), pp.2655-2675
- 17) F. Li, On the negative-order norm accuracy of a local-structure-preserving LDG method, [PDF], Journal of Scientific Computing, v51 (2012), pp.213-223
- 16) F. Li, L. Xu, S. Yakovlev, Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field, [PDF], Journal of Computational Physics, v230 (2011), pp.4828-4847. (Correction: in section 4.2.6, it is `with the darker area representing the smaller value)
- 15) W. Guo, F. Li, J. Qiu, Local-structure-preserving discontinuous Galerkin methods with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations, [PDF], Journal of Scientific Computing, v47 (2011), pp.239-257
- 14) Y.-T. Zhang, S. Chen, F. Li, H.-K. Zhao, C.-W. Shu, Uniformly accurate discontinuous Galerkin fast sweeping methods for Eikonal equations, [PDF], SIAM Journal on Scientific Computing, v33 (2011), pp.1873-1896
- 13) B. Cockburn, J. Gopalakrishnan, F. Li, N.-C. Nguyen, J. Peraire, Hybridization and postprocessing techniques for mixed eigenfunctions, [PDF] , SIAM Journal on Numerical Analysis, v48 (2010), pp.857-881
- 12) F. Li and S. Yakovlev, A central discontinuous Galerkin method for Hamilton-Jacobi equations, [PDF], Journal of Scientific Computing, v45 (2010), pp.404-428. (Special issue in memory of Professor David Gottlieb)
- 11) S. C. Brenner, F. Li, L.-Y. Sung, Nonconforming Maxwell eigensolvers, [PDF], Journal of Scientific Computing, v40 (2009), pp.51-85
- 10) S. C. Brenner, F. Li, L.-Y. Sung, A nonconforming penalty method for a two-dimensional curl-curl problem, [PDF], Mathematical Models and Methods in Applied Mathematics, v19 (2009), pp.651-668
- 9) F. Li, C.-W. Shu, Y.-T. Zhang, H.-K. Zhao, A second order DGM based fast sweeping method for Eikonal equations, [PDF] Journal of Computational Physics, v227 (2008), pp.8191-8208
- 8) S. C. Brenner, J. Cui, F. Li, L.-Y. Sung, A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem, [PDF] Numerische Mathematik, v109 (2008), pp.509-533
- 7) S. C. Brenner, F. Li, L.-Y. Sung, A locally divergence-free interior penalty method for two-dimensional curl-curl problems, [PDF] SIAM Journal on Numerical Analysis, v46 (2008), pp.1190-1211
- 6) S. C. Brenner, F. Li, L.-Y. Sung, A locally divergence-free nonconforming finite element method for the reduced time-harmonic Maxwell equations, [PDF] Mathematics of Computation, v76 (2007), pp.573-595
- 5) F. Li and C.-W. Shu, A local-structure-preserving local discontinuous Galerkin method for the Laplace equation, [PDF] [Some Correction] Methods and Applications of Analysis, v13 (2006), pp.215-233 (Special issue dedicated to Professor Bjorn Engquist on the occasion of his 60th birthday)
- 4) F. Li and C.-W. Shu, Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations, [PDF] Applied Mathematics Letters, v18 (2005), pp.1204-1209
- 3) F. Li and C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for MHD equations, [PDF] Journal of Scientific Computing, v22-23 (2005), pp.413-442
- 2) B. Cockburn, F. Li, C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for the Maxwell equations, [PDF] Journal of Computational Physics, v194 (2004), pp.588-610
- 1) L.-A. Ying and F. Li, Exterior Problem of the Darwin Model and its Numerical Computation, [PDF] ESAIM: Mathematical Modelling and Numerical Analysis, v37 (2003), pp.515-532

- Refereed Book Chapters

- B1) Y. Chen, Z. Chen, Y. Cheng, A. Gillman, and F. Li, Study of discrete scattering operators for some linear kinetic models, [PDF], The IMA Volumes in Mathematics and its Applications, Vol. 160 (2016), Susanne Brenner (Ed): Topics in Numerical Partial Differential Equations and Scientific Computing, pp.99-136, Springer.

- Publications in Conference and Workshop Proceedings

- [2] S. C. Brenner, F. Li and L.-Y. Sung, A locally divergence-free nonconforming finite element method for the reduced time-harmonic Maxwell equations, [PDF] Proceedings of the joint Workshop by AWM and MSRI: The Legacy of Ladyzhenskaya and Oleinik, 2006, pp.187-191
- [1] B. Cockburn, F. Li and C.-W. Shu, Discontinuous Galerkin methods for equations with divergence-free solutions: preliminary results, the proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, K.J. Bathe, Editor, June 2003, Elsevier Science, pp.1900-1902

- Research report

- F. Li, A priori error estimates of a local-structure-preserving LDG method, [PDF], May 2011